Abstract
A nexperiment involving a complex computer model or code may have tens or even hundreds of input variables and, hence, the identification of the more important variables (screening) is often crucial. Methods are described for decomposing a complex input—output relationship into effects. Effects are more easily understood because each is due to only one or a small number of input variables. They can be assessed for importance either visually or via a functional analysis of variance. Effects are estimated from flexible approximations to the input—output relationships of the computer model. This allows complex nonlinear and interaction relationships to be identified. The methodology is demonstrated on a computer model of the relationship between environmental policy and the world economy.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Akaike, H. (1973). Information theory and an extension of the maximum likelihood principle. In Second International Symposium on Information Theory, pages 267–281. Akademia Kiadó, Budapest.
Aslett, R., Buck, R.J., Duvall, S.G., Sacks, J., and Welch, W.J. (1998). Circuit optimization via sequential computer experiments: Design of an output buffer. Journal of the Royal Statistical Society, C, 47, 31–48.
Bernardo, M.C., Buck, R., Liu, L., Nazaret, W.A., Sacks, J., and Welch, W.J. (1992). Integrated circuit design optimization using a sequential strategy. IEEE Transactions on Computer-Aided Design, 11, 361–372.
Bettonvil, B. and Kleijnen, J.P.C. (1996). Searching for important factors in simulation models with many factors: Sequential bifurcation. European Journal of Operational Research, 96, 180–194.
Chapman, W.L., Welch, W.J., Bowman, K.P., Sacks, J., and Walsh, J.E. (1994). Arctic sea ice variability: Model sensitivities and a multidecadal simulation. Journal of Geophysical Research C, 99, 919–935.
Currin, C., Mitchell, T., Morris, M., and Ylvisaker, D. (1991). Bayesian prediction of deterministic functions, with applications to the design and analysis of computer experiments. Journal of the American Statistical Association, 86, 953–963.
Gough, W.A. and Welch, W.J. (1994). Parameter space exploration of an ocean general circulation model using an isopycnal mixing parameterization. Journal of Marine Research, 52, 773–796.
Gu, C. and Wahba, G. (1993). Smoothing spline ANOVA with componentwise Bayesian “confidence intervals”. Journal of Computational and Graphical Statistics, 2, 97–117.
Herbert, R.D. and Leeves, G.D. (1998). Troubles in Wonderland. Complexity International, 6. http://www.complexity.org.au/ci/vol06/herbert/herbert.html
Hoeffding, W. (1948). A class of statistics with asymptotically normal distribution. The Annals of Mathematical Statistics, 19, 293–325.
Iman, R.L. and Conover, W.J. (1980). Small sample sensitivity analysis techniques for computer models, with an application to risk assessment. Communications in Statistics A—Theory and Methods, 9, 1749–1842.
Jones, D.R., Schonlau, M., and Welch, W.J. (1998). Efficient global optimization of expensive black-box functions. Journal of Global Optimization, 13, 455–492.
Koehler, J.R. and Owen, A.B. (1996). Computer experiments. In Handbook of Statistics, Volume 13. Editors: S. Ghosh and C.R. Rao. Elsevier, Amsterdam.
Lempert, R.J., Popper, S.W., and Bankes, S.C. (2003). Shaping the Next One Hundred Years: New Methods for Quantitative, Long-term Policy Analysis. RAND, Santa Monica, CA. http://www.rand.org/publications/MR/MR1626
McKay, M.D., Conover, W.J., and Beckman, R.J. (1979). A comparison of three methods for selecting values of input variables in the analysis of output from a computer code. Technometrics, 21, 239–245.
Morris, M.D. (1991). Factorial sampling plans for preliminary computer experiments. Technometrics, 33, 161–174.
Mrawira, D., Welch, W.J., Schonlau, M., and Haas, R. (1999). Sensitivity analysis of computer models: World Bank HDM-III model. Journal of Transportation Engineering, 125, 421–428.
R Development Core Team (2005). R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing, Vienna. http://www.R-project.org
Robert, C.P. and Casella, G. (2004). Monte Carlo Statistical Methods, second edition. Springer, New York.
Sacks, J., Welch, W.J., Mitchell, T.J., and Wynn, H.P. (1989). Design and analysis of computer experiments (with discussion). Statistical Science, 4, 409–435.
Santner, T.J., Williams, B.J., and Notz, W.I. (2003). The Design and Analysis of Computer Experiments. Springer Verlag, New York.
Schonlau, M. (1997). Computer experiments and global optmization. PhD thesis, University of Waterloo, Waterloo, Ontario.
Welch, W.J., Buck, R.J., Sacks, J., Wynn, H.P., Mitchell, T.J., and Morris, M.D. (1992). Screening, predicting, and computer experiments. Technometrics, 34, 15–25.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2006 Springer Science+Business Media, Inc.
About this chapter
Cite this chapter
Schonlau, M., Welch, W.J. (2006). Screening the Input Variables to a Computer Model Via Analysis of Variance and Visualization. In: Dean, A., Lewis, S. (eds) Screening. Springer, New York, NY. https://doi.org/10.1007/0-387-28014-6_14
Download citation
DOI: https://doi.org/10.1007/0-387-28014-6_14
Publisher Name: Springer, New York, NY
Print ISBN: 978-0-387-28013-4
Online ISBN: 978-0-387-28014-1
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)